Finite Group Databasebeta

← Prev (#36339330) Next (#36339332) →

C32×C17×Dic35 #36339331

order21420
automorphism?
homologyAbelianization (H1) = C32×C4×C17 · Schur multiplier (H2) = C3

Aliases

direct productC32×C17×Dic35

Splittings

derived, HallC5×C7 ⋊ C32×C4×C17
HallC32×C5×C7×C17 ⋊ C4
HallC32×C7×C17 ⋊ Dic5
HallC32×C5×C17 ⋊ Dic7
HallC5×C7×C17 ⋊ C32×C4
HallC32×C5×C7 ⋊ C4×C17
HallC7×C17 ⋊ C32×Dic5
HallC5×C17 ⋊ C32×Dic7
HallC32×C7 ⋊ C17×Dic5
HallC32×C5 ⋊ C17×Dic7
SylowC7 ⋊ C32×C17×Dic5
SylowC5 ⋊ C32×C17×Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C32×C17D35
commutator, hypocenterC5×C7C32×C4×C17
FrattiniC2C32×C17×D35
Fitting, socle, prime radicalC2×C32×C5×C7×C17C2
cosocleC2×C5×C7C2×C32×C17
LCSG ▷ C5×C7
UCSC1 ◁ C2×C32×C17

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21420

Conjugacy classes & character table

5814 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 163);